A159969 Numerator of Hermite(n, 13/24).

1, 13, -119, -9035, -14639, 10218013, 153914329, -15655840187, -513817209695, 29391432064813, 1713902824372009, -62366587629825323, -6240409786798253711, 134413599620299018045, 25111471036836549128569, -215506510190170502086043, -111283139511606108762536639

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..428

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 12^n * Hermite(n, 13/24).

E.g.f.: exp(13*x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 13/12, -119/144, -9035/1728, -14639/20736, ...

Mathematica

Numerator[Table[HermiteH[n, 13/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A001021 (denominators).

Sequence in context: A367244 A016285 A121086 * A253512 A295048 A295376

Adjacent sequences: A159966 A159967 A159968 * A159970 A159971 A159972

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved